Gauging spacetime inversions in quantum gravity

Understand

Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries.

• In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries.
• In particular this includes $\mathcal{CRT}$ symmetry (in even dimensions usually combined with a rotation to become $\mathcal{CPT}$), which in quantum field theory is always a symmetry and seems likely to be a symmetry of quantum gravity as well.
• In this article we discuss what it means to gauge a spacetime inversion symmetry, and we explain some of the more unusual consequences of doing this.